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Modeling geometric non-linearities in the free vibration of a planar beam flexure with a tip mass

Moeenfard, H ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1115/DETC2012-71498
  3. Publisher: 2012
  4. Abstract:
  5. The objective of this work is to create an analytical framework to study the non-linear dynamics of beam flexures with a tip mass undergoing large deflections. Hamilton's principal is utilized to derive the equations governing the nonlinear vibrations of the cantilever beam and the associated boundary conditions. Then, using a single mode approximation, these non-linear partial differential equations are reduced to two coupled non-linear ordinary differential equations. These equations are solved analytically using combination of the method of multiple time scales and homotopy perturbation analysis. Closed-form, parametric analytical expressions are presented for the time domain response of the beam around and far from its internal resonance state. These analytical results are compared with numerical ones to validate the accuracy of the proposed closed-form model. We expect that the qualitative and quantitative knowledge resulting from this effort will ultimately allow the analysis, optimization, and synthesis of flexure mechanisms for improved dynamic performance
  6. Keywords:
  7. Analytical expressions ; Geometric nonlinearity ; Non-linear vibrations ; Nonlinear ordinary differential equation ; Nonlinear partial differential equations ; Perturbation Analysis ; Quantitative knowledge ; Single-mode approximation ; Mechanisms ; Design
  8. Source: Proceedings of the ASME Design Engineering Technical Conference, 12 August 2012 through 12 August 2012 ; Volume 4, Issue PARTS A AND B , August , 2012 , Pages 363-371 ; 9780791845035 (ISBN)
  9. URL: http://proceedings.asmedigitalcollection.asme.org/proceeding.aspx?articleid=1736482